We look at the division of 678559 by 45 
We want to divide 678559 by 45.

Advancing to step 1:
When dividing 6 by 45, we get 0 with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Take the next digit (7) from the dividend and append it to 6, then repeat: 67 / 45

Moving on to step 2:
45 goes into 67 1 times with a remainder of 22.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 45 from 67 and we're left with 22.
Take the next digit (8) from the dividend and append it to 22, then repeat: 228 / 45

Step 3:
228 divided by 45 is 5 with a remainder of 3.
Put 5 as the next digit of the answer. 
Result so far: 15.0
Deduct 225 from 228 and we're left with 3.
Append the next digit (5) from the dividend to 3 and continue with: 35 / 45

Going ahead to step 4:
The number 45 fits into 35 0 times, leaving a remainder of 35.
Write down 0 as next digit of the result. 
Result so far: 150.0
The remainder is 35 after subtracting 0 from 35.
Fetch the next digit (5) from the dividend, attach it to 35 and continue: 355 / 45

On to step 5:
45 goes into 355 7 times with a remainder of 40.
The next digit of our result is 7. 
Result so far: 1507.0
If we subtract 315 from 355, we get 40.
Grab the next digit (9) from the dividend, add it to 40, then carry on: 409 / 45

Going ahead to step 6:
The number 45 fits into 409 9 times, leaving a remainder of 4.
The next digit of our result is 9. 
Result so far: 15079.0
If we subtract 405 from 409, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 7:
40 divided by 45 is 0 with a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 15079.0
If we subtract 0 from 40, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Let's proceed to step 8:
45 can be fit into 400 8 times, resulting in a remainder of 40.
Write down 8 as next digit of the result. 
Result so far: 15079.08
The remainder is 40 after subtracting 360 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 9:
If we divide 400 by 45, we get 8 and a remainder of 40.
The number 8 becomes the next digit in our result. 
Result so far: 15079.088
If we take 360 away from 400, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

The final result is 15079.088 with a remainder of 0.004.